The transposition reaction of bacteriophage Mu and HIV DNA integration reaction are studied in this project. Critical steps in these reactions are a pair of DNA cleavages and strand transfers involving the ends of Mu or HIV DNA sequence and a target DNA;these reactions generate branched DNA intermediates. The two chemical reaction steps take place within higher order protein-DNA complexes called transpososome or preintegration complex, the core of which is composed of two end segments of the transposing donor DNA synapsed by a tetramer of MuA transposase or HIV IN protein. The assembly of these higher order protein-DNA complexes and the catalytic activities of the protein within the assembled complex are controlled by a variety of factors, not all of which are well understood. This project aims to advance our understanding of how the viral DNA integration processes are controlled by the structural components and their dynamic interactions within the complex. We have shown that both the Mu end DNA cleavage and the subsequent strand transfer at one Mu DNA end are catalyzed by the MuA monomer that is bound to the partner Mu DNA end within a transpososome. By comparing the activity of chiral phosphorothioate containing DNA substrates, we could monitor the mode of interactions between the substrate DNA and the transposase active site throughout the successive reaction steps. The results of this study led to a mechanistic model that explained how the successive reaction steps involved in the DNA insertion take place within the higher order complex. The molecular interactions involved in Mu transposition complex and HIV preintegration complex have been studied by using fluorescence labeled proteins and DNA substrates. Fluorescence-based tools have been developed for the assay of the Mu transposase-DNA binding, Mu-end pairing, stable synaptic complex formation, and Mu-end DNA deformation. Similar fluorescence-based tools for the study of HIV preintegration complex are under development. We have developed FRET based tools for the analysis of the higher order complexes involved in these reactions, and advances have been made on the methods for the FRET data analysis in order to improve the information quality obtained. HIV DNA within a preintegration complex is protected by BAF protein, which is believed to condense the DNA in such a way to make it inaccessible for self-destructive auto-integration. The mechanism of DNA condensation by BAF has been studied at single DNA-molecule level by using fluorescence labeled BAF and a high-sensitivity fluorescence microscope system. Kinetic properties of the protein-DNA interaction and DNA condensation have been investigated.